MinT - Best Known (25, 35, s)-Nets in Base 3

Best Known (25, 35, s)-Nets in Base 3

(25, 35, 114)-Net over F₃ — Constructive and digital

Digital (25, 35, 114)-net over F₃, using

1 times m-reduction [i] based on digital (25, 36, 114)-net over F₃, using
- trace code for nets [i] based on digital (1, 12, 38)-net over F₂₇, using
  - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(25, 35, 194)-Net over F₃ — Digital

Digital (25, 35, 194)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³⁵, 194, F₃, 10) (dual of [194, 159, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3³⁵, 242, F₃, 10) (dual of [242, 207, 11]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(25, 35, 2844)-Net in Base 3 — Upper bound on s

There is no (25, 35, 2845)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 50096 774786 371659 > 3³⁵ [i]